A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 30 degree. From a point 1500 feet closer to the mountain along the plain, they find that the angle of elevation is 34 degree.
How high (in feet) is the mountain?
2007-06-21 17:44:16 · 2 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
Draw a figure.
Original distance from the mountain = x
Height = h
h/x = tan 30
h/(x-1500) = tan 34
tan 30 / tan 34 = (x-1500)/x
1 - 1500/x = 0.8560
x = 10414
h = 10417*tan30 = 6012ft
The height of the mountain is just over 6000 feet
2007-06-21 17:50:39 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
The height of the mountain is H.
The distance to the closer vantage point is D.
The distance to the farther vantage point is D + 1500.
H is opposite the surveyed angle, and D/D+1500 is adjacent.
So tan(34) = H/D
H = D tan(34)
tan(30) = H/(D + 1500)
H = (D + 1500)tan(30)
D tan (34) = (D + 1500) tan(30)
D tan (34) = D tan (30) + 1500 tan (30)
D tan (34) - D tan (30) = 1500 tan (30)
D = 1500 tan (30) / (tan (34) - tan (30))
D = (1500 * 0.577) / (0.674 - 0.577)
D = 866 / 0.097
D = 8914
H = D tan(34)
H = 8914 * 0.674
H = 6,012 ft
2007-06-22 00:54:58 · answer #2 · answered by TychaBrahe 7 · 1⤊ 0⤋